Scale-free mobility

Some ideas feel like an itch that you can't quite scratch because it's hard to pin down, but you really want to. A recent paper by Young et al. in Nature Physics (and available here), along with a commentary by Brockmann feels a little bit like that - at least when seen through the soupy goggles of astrobiology. On the surface this paper appears pretty innocent. It studies the nature of human mobility. With the rise of data-logging; from global positioning, cell-phone records, and the colossal airline databases of 3 billion annual travelers there is unprecedented material for studying exactly how we move around the planet. Not surprisingly we exhibit particular statistical patterns. For both distances traveled and 'rest times' (how long we linger over a cup of coffee or beneath the umbrella of some tropical beach) the distributions are inverse power laws. In plain language this means that we are more likely to travel short distances and to spend little time in any one place during travel.

There's nothing that sounds particularly revolutionary about that. But it gets more interesting. As Young et al. discuss, the particular shape of the statistics appears to be modeled rather well with a form of 'preferential return'. In other words although we may explore - making new journeys - we are more likely to travel to locations that we already know.  Not only that but the more locations that we already know the less likely we are to explore new ones at all. This naturally produces a so-called scale-free distribution - if you go out to any particular pub then there will be another pub that you are twice as likely to visit, and another one that is half as likely to have your patronage. The Young et al. model boils down to assigning a probability for any given 'step' in an individual's travels that results in exploration (a new location). They give this as the number of prior travel steps to the inverse-power of....0.2.

Why 0.2 ? Nobody knows, but this describes the way human populations explore the world - individuals will deviate from this pattern, but en-masse this is what we do. It's a deceptively simple, but extremely provocative result. Does this same kind of probabilistic scaling apply to other species? Do other species have a different power law value than 0.2? What are the implications for the occupation of niches by organisms on a planetary scale and throughout the history of life? This implicit tendency for exploration to slow down in favor of re-visiting known locations makes me wonder about a recent discovery on the global East-West divide in marine microbial genetics. While environmental differences are the most obvious root bio-physical cause (particularly the differing soluble phosphorus amounts in the Atlantic vs. Pacific oceans), does this give rise to a similar 'preferential return' scaling?

Then, to return to a popular theme - is there something to be learnt from this model for the questions of life exploring the cosmos beyond a planetary homeworld? On the face of it the more you explore the more likely you are to slow down and just keep circulating amongst the places you know. Clearly the present data represents humans who are not, we presume, exploring for survival or vital resources - lattes don't count. Nonetheless it is reasonable to hypothesize that humans behave this way because there is some circumstantial evolutionary advantage to it. The hard-to-pin-down-itch is that one suspects there is something deeper - perhaps universal -  in all this, waiting to be ferreted out.